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Diffstat (limited to 'lib/divsf3.c')
| -rw-r--r-- | lib/divsf3.c | 168 |
1 files changed, 0 insertions, 168 deletions
diff --git a/lib/divsf3.c b/lib/divsf3.c deleted file mode 100644 index c91c648fa24cf..0000000000000 --- a/lib/divsf3.c +++ /dev/null @@ -1,168 +0,0 @@ -//===-- lib/divsf3.c - Single-precision division ------------------*- C -*-===// -// -// The LLVM Compiler Infrastructure -// -// This file is dual licensed under the MIT and the University of Illinois Open -// Source Licenses. See LICENSE.TXT for details. -// -//===----------------------------------------------------------------------===// -// -// This file implements single-precision soft-float division -// with the IEEE-754 default rounding (to nearest, ties to even). -// -// For simplicity, this implementation currently flushes denormals to zero. -// It should be a fairly straightforward exercise to implement gradual -// underflow with correct rounding. -// -//===----------------------------------------------------------------------===// - -#define SINGLE_PRECISION -#include "fp_lib.h" - -ARM_EABI_FNALIAS(fdiv, divsf3) - -fp_t __divsf3(fp_t a, fp_t b) { - - const unsigned int aExponent = toRep(a) >> significandBits & maxExponent; - const unsigned int bExponent = toRep(b) >> significandBits & maxExponent; - const rep_t quotientSign = (toRep(a) ^ toRep(b)) & signBit; - - rep_t aSignificand = toRep(a) & significandMask; - rep_t bSignificand = toRep(b) & significandMask; - int scale = 0; - - // Detect if a or b is zero, denormal, infinity, or NaN. - if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) { - - const rep_t aAbs = toRep(a) & absMask; - const rep_t bAbs = toRep(b) & absMask; - - // NaN / anything = qNaN - if (aAbs > infRep) return fromRep(toRep(a) | quietBit); - // anything / NaN = qNaN - if (bAbs > infRep) return fromRep(toRep(b) | quietBit); - - if (aAbs == infRep) { - // infinity / infinity = NaN - if (bAbs == infRep) return fromRep(qnanRep); - // infinity / anything else = +/- infinity - else return fromRep(aAbs | quotientSign); - } - - // anything else / infinity = +/- 0 - if (bAbs == infRep) return fromRep(quotientSign); - - if (!aAbs) { - // zero / zero = NaN - if (!bAbs) return fromRep(qnanRep); - // zero / anything else = +/- zero - else return fromRep(quotientSign); - } - // anything else / zero = +/- infinity - if (!bAbs) return fromRep(infRep | quotientSign); - - // one or both of a or b is denormal, the other (if applicable) is a - // normal number. Renormalize one or both of a and b, and set scale to - // include the necessary exponent adjustment. - if (aAbs < implicitBit) scale += normalize(&aSignificand); - if (bAbs < implicitBit) scale -= normalize(&bSignificand); - } - - // Or in the implicit significand bit. (If we fell through from the - // denormal path it was already set by normalize( ), but setting it twice - // won't hurt anything.) - aSignificand |= implicitBit; - bSignificand |= implicitBit; - int quotientExponent = aExponent - bExponent + scale; - - // Align the significand of b as a Q31 fixed-point number in the range - // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax - // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2. This - // is accurate to about 3.5 binary digits. - uint32_t q31b = bSignificand << 8; - uint32_t reciprocal = UINT32_C(0x7504f333) - q31b; - - // Now refine the reciprocal estimate using a Newton-Raphson iteration: - // - // x1 = x0 * (2 - x0 * b) - // - // This doubles the number of correct binary digits in the approximation - // with each iteration, so after three iterations, we have about 28 binary - // digits of accuracy. - uint32_t correction; - correction = -((uint64_t)reciprocal * q31b >> 32); - reciprocal = (uint64_t)reciprocal * correction >> 31; - correction = -((uint64_t)reciprocal * q31b >> 32); - reciprocal = (uint64_t)reciprocal * correction >> 31; - correction = -((uint64_t)reciprocal * q31b >> 32); - reciprocal = (uint64_t)reciprocal * correction >> 31; - - // Exhaustive testing shows that the error in reciprocal after three steps - // is in the interval [-0x1.f58108p-31, 0x1.d0e48cp-29], in line with our - // expectations. We bump the reciprocal by a tiny value to force the error - // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to - // be specific). This also causes 1/1 to give a sensible approximation - // instead of zero (due to overflow). - reciprocal -= 2; - - // The numerical reciprocal is accurate to within 2^-28, lies in the - // interval [0x1.000000eep-1, 0x1.fffffffcp-1], and is strictly smaller - // than the true reciprocal of b. Multiplying a by this reciprocal thus - // gives a numerical q = a/b in Q24 with the following properties: - // - // 1. q < a/b - // 2. q is in the interval [0x1.000000eep-1, 0x1.fffffffcp0) - // 3. the error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes - // from the fact that we truncate the product, and the 2^27 term - // is the error in the reciprocal of b scaled by the maximum - // possible value of a. As a consequence of this error bound, - // either q or nextafter(q) is the correctly rounded - rep_t quotient = (uint64_t)reciprocal*(aSignificand << 1) >> 32; - - // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0). - // In either case, we are going to compute a residual of the form - // - // r = a - q*b - // - // We know from the construction of q that r satisfies: - // - // 0 <= r < ulp(q)*b - // - // if r is greater than 1/2 ulp(q)*b, then q rounds up. Otherwise, we - // already have the correct result. The exact halfway case cannot occur. - // We also take this time to right shift quotient if it falls in the [1,2) - // range and adjust the exponent accordingly. - rep_t residual; - if (quotient < (implicitBit << 1)) { - residual = (aSignificand << 24) - quotient * bSignificand; - quotientExponent--; - } else { - quotient >>= 1; - residual = (aSignificand << 23) - quotient * bSignificand; - } - - const int writtenExponent = quotientExponent + exponentBias; - - if (writtenExponent >= maxExponent) { - // If we have overflowed the exponent, return infinity. - return fromRep(infRep | quotientSign); - } - - else if (writtenExponent < 1) { - // Flush denormals to zero. In the future, it would be nice to add - // code to round them correctly. - return fromRep(quotientSign); - } - - else { - const bool round = (residual << 1) > bSignificand; - // Clear the implicit bit - rep_t absResult = quotient & significandMask; - // Insert the exponent - absResult |= (rep_t)writtenExponent << significandBits; - // Round - absResult += round; - // Insert the sign and return - return fromRep(absResult | quotientSign); - } -} |